Related papers: Tensor Network Renormalization
Recurrent neural networks (RNNs) are powerful tools for sequential modeling, but typically require significant overparameterization and regularization to achieve optimal performance. This leads to difficulties in the deployment of large…
Real-space renormalization-group techniques for quantum systems can be divided into two basic categories - those capable of representing correlations following a simple boundary (or area) law, and those which are not. I discuss the scaling…
Tensor networks have proven to be a valuable tool, for instance, in the classical simulation of (strongly correlated) quantum systems. As the size of the systems increases, contracting larger tensor networks becomes computationally…
Recently, it has been claimed that some complex networks are self-similar under a convenient renormalization procedure. We present a general method to study renormalization flows in graphs. We find that the behavior of some variables under…
Tensor network contraction is central to problems ranging from many-body physics to computer science. We describe how to approximate tensor network contraction through bond compression on arbitrary graphs. In particular, we introduce a…
Tensor network techniques are becoming increasingly popular tools to solve partial differential equations within the so-called quantics representation. Their popularity stems from the fact that their spatial resolution depends only…
We review recent developments in tensor network approaches, focusing on renormalization group methods. Since they are free from the negative sign and complex action problems, there is growing interest in their application to lattice field…
When studying interacting systems, computing their statistical properties is a fundamental problem in various fields such as physics, applied mathematics, and machine learning. However, this task can be quite challenging due to the…
Tensor renormalization group method (TRG) is a real space renormalization group approach. It has been successfully applied to both classical and quantum systems. In this paper, we study a disordered and frustrated system, the…
We show how to build a multi-scale entanglement renormalization ansatz (MERA) representation of the ground state of a many-body Hamiltonian $H$ by applying the recently proposed \textit{tensor network renormalization} (TNR) [G. Evenbly and…
Understanding dissipation in 2D quantum many-body systems is a remarkably difficult open challenge. Here we show how numerical simulations for this problem are possible by means of a tensor network algorithm that approximates steady-states…
We introduce a class of variational states to describe quantum many-body systems. This class generalizes matrix product states which underly the density-matrix renormalization group approach by combining them with weighted graph states.…
This paper demonstrates a method for tensorizing neural networks based upon an efficient way of approximating scale invariant quantum states, the Multi-scale Entanglement Renormalization Ansatz (MERA). We employ MERA as a replacement for…
We investigate the entanglement spectrum in HOTRG ---tensor renormalization group (RG) method combined with the higher order singular value decomposition--- for two-dimensional (2D) classical vertex models. In the off-critical region, it is…
Coarse-grained models are a core computational tool in theoretical chemistry and biophysics. A judicious choice of a coarse-grained model can yield physical insight by isolating the essential degrees of freedom that dictate the…
Tensor networks have emerged as promising tools for machine learning, inspired by their widespread use as variational ansatze in quantum many-body physics. It is well known that the success of a given tensor network ansatz depends in part…
The physical properties of a quantum many-body system can, in principle, be determined by diagonalizing the respective Hamiltonian, but the dimensions of its matrix representation scale exponentially with the number of degrees of freedom.…
Quantum processing units boost entanglement at the level of hardware and enable physical simulations of highly correlated electron states in molecules and intermolecular chemical bonds. The variational quantum eigensolver provides a…
Quantum simulators have the potential to solve quantum many-body problems that are beyond the reach of classical computers, especially when they feature long-range entanglement. To fulfill their prospects, quantum simulators must be fully…
We present tensor networks for feature extraction and refinement of classifier performance. These networks can be initialised deterministically and have the potential for implementation on near-term intermediate-scale quantum (NISQ)…